To determine how many tickets Joseph can buy, we first need to calculate how much money he has left after buying the hat.
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Subtract the cost of the hat from Joseph's total amount: \[ 34.25 - 12.50 = 21.75 \]
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Now, we need to see how many tickets he can buy with the remaining amount. Each ticket costs 7.25. We divide the remaining amount by the cost of a ticket: \[ 21.75 \div 7.25 \approx 3 \]
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To confirm, we can multiply the number of tickets by the ticket price and see if it stays within his budget: \[ 3 \times 7.25 = 21.75 \]
Since the total cost of 3 tickets (21.75) matches the remaining amount he has after buying the hat, Joseph can buy 3 tickets.